| 一维有限元后处理超收敛解答计算的EEP法 |
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| 引用本文： | 袁驷,王枚.一维有限元后处理超收敛解答计算的EEP法[J].工程力学,2004,21(2):1-9. |
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| 作者姓名： | 袁驷 王枚 |
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| 作者单位： | 清华大学土木工程系,北京,100084 |
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| 基金项目： | 国家自然科学基金资助项目(50278046) |
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| 摘 要： | 提出一维有限元法后处理中超收敛解答的一种自然合理的算法,称为单元能量投影法(EEP)。理论分析和数值算例表明,提出的方法简便易行、行之有效、效果显著;此外,还有一些颇合人意的优点,如:任一点的应力和位移的误差与结点位移的误差具有相同的收敛阶(m次单元可达mh2阶)、结点两边单元各自算出的应力自动平衡、自由端点的应力自动为精确值等。
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| 关 键 词： | 有限元 一维问题 后处理 超收敛 单元能量投影 |
| 文章编号： | 1000-4750(2004)02-0001-09 |
| 修稿时间： | 2002年12月5日 |
AN ELEMENT-ENERGY-PROJECTION METHOD FOR POST-COMPUTATION OF SUPER-CONVERGENT SOLUTIONS IN ONE-DIMENSIONAL FEM |
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| YUAN Si,WANG Mei.AN ELEMENT-ENERGY-PROJECTION METHOD FOR POST-COMPUTATION OF SUPER-CONVERGENT SOLUTIONS IN ONE-DIMENSIONAL FEM[J].Engineering Mechanics,2004,21(2):1-9. |
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| Authors: | YUAN Si WANG Mei |
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| Abstract: | The present paper presents, for one-dimensional FEM at the present stage, a natural and rational approach called Element Energy Projection (EEP) method for super-convergent calculation of both displacements and stresses at any point in an element in post-processing stage. The proposed method is simple, effective and efficient. A large number of numerical examples consistently show that the accuracy of both displacements and stresses so calculated is well comparable to that of the nodal displacements, i.e. being of order mh2 for elements of degree m with sufficiently smooth solutions. |
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| Keywords: | FEM one-dimensional problem post-processing super-convergence element energy projection |
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